The Regularity Of Continuous Operators On Al-Spaces

In this paper, we present the generalized result about the regularity of operators. The relations between regularity and modulus are studied, and when the spaces have some completion, they are equivalent, otherwise some counterexamples are given. The regularity of operators on finite dimensional Riesz spaces and the matrix means of these operators are obtained. In addition, some examples are given to show that operators on infinite dimensional spaces have not this similar properties.The main purpose of the thesis is to study the regularity of contin-ous operators on AL-spaces. Here we present a characterization on AL-spaces E such that every bounded linear operator from E into a Banach lattice is regular. Moreover under this condition the space of regular operators is a lattice.Finally, we survey the regularity of some special operators, such as compact and weakly compact operators. We conclued some results by investigating the regularity and modulus of these operators on AL-spaces, AM-spaces or KB-spaces.